Dr. James C.Y. Guo, P.E., Professor and Director Civil Engineering, U. of Colorado Denver Pitot-Static Tube

Transcription

1 Flow Measurement Dr. James C.Y. Guo, P.E., Professor and Dretor Cvl Engneerng, U. of Colorado Denver Ptot-Stat Tube 1

2 Ptot-tube for Veloty Measurement Operaton of Ptot-Tube

3 Manometer and Pressure Dfferental Example of Flow Veloty Measurement The ar flow s arred n a 1-nh rular ppe. The ar flow s at 70 o F and under an atmospher pressure of 1.4 ps. The ptot-tube s used to measure the ar flow veloty at the enterlne. The pressure dfferental s measured to be 3 nhes n a water manometer. Fnd the enterlne veloty. w h a ( 1) a = γ γ h w 3

4 Measurement of Flow Rate veloty n feet/se Radus ft Example of Ar Flow Veloty Contours Loaton Measured Average Crle Rng Inremental Aum from Ar Flow Flow Area Area Flow Flow Ppe Cntr Veloty Veloty m mps mps sq m sq m mps mps Calulate the ross setonal average veloty Calulate the rato of the enter veloty to average veloty 4

5 Revew of Turbulent Flow Veloty Profle R R u = U m.5u* ln = U m 5.76u* log () R r R r Eq has two unknown: U m and u *. U m = V ( f ) 1. V (3) τ u = = V ρ * f 8 (4) 5

6 Example of Flow Veloty Measurement 4.1 A 10-ft ppe arres a water flow of 1000 fs. The frton fator for ths ase s Analyze ths flow. (1) Cross seton area A = 78.5 sq ft () () Flow veloty V = 1.73 fps (3) Centerlne veloty U m = ( f ) V = 1.3V = fps (V/U m = 0.81) τ f (4) Shear veloty u* = = V = fps ρ 8 (5) Shear stress τ = lb/ft 5 (6) u = ln( ) 5 r Flow Measurement: Centerlne Veloty Approah A ptot-tube s used to measure the enterlne veloty n a 1- nh rular ppe that has a frton fator f of 0.05 Calulate the enterlne veloty Fnd the average veloty Calulate the flow rate. 6

7 Ventur Meter Q = AV = A gh Q a Q K = Q a = KA gh Orfe Meter Q = AV = A Q = KA a Q K = Q a gh gh Q a Q 7

8 Orfe Outlet Orfe = an openng on a wall Nozzle = a short onvertng ppe Jet = a hgh-speed stream of flow ssued from a nozzle 8

9 Orfe Outlet Equaton A C = A V Cv = V a Q = AV = A K = C C Q = AV = C AC v gh v gh = KA gh Q = KA o o g( Y Y ) Examples of Orfe Outlet 9

10 Wer Hydrauls End Contraton Q = C d g ( L 0.1 n H ) H = C L H w e 1.5 C d =

11 Examples of Orfe Outlet An openng area n the flow feld an be vertal, horzontal, or nlned. Ths openng area may be operated lke an orfe when the entre openng area s submerged or operated lke a wer f the openng area s partally submerged. Q=mn (Q wer, Q orfe ) for a gven depth Example for Wer Flow Fnd the release flow rate through the vertal orfe (1) when the water surfae elevaton at 500 ft () when the water surfae elevaton at 5006 ft 11

12 Roadway Culvert V Noth 1

13 Slue Gate Q = C s A gy C s =0.5 to 0.6 OPEN CHANNEL FLOW 1. Bottom Wdth B. Sde Slope Z 3. Top Wdth T= B + Z Y 4. Area A = 0.5 (T+B)Y 5. Wetted Permeter P = B + Y(1+Z ) Hydraul Radus R = A/P 7. Hydraul Depth D = A/T 8. Froude Number Fr = U/(gD)

14 Example: Channel Seton Element A symmetral trapezodal hannel has a bottom wdth of 0 ft, sde slope of 1V:5H (Z= 5), and flow depth of feet. Fnd the flow area, top wdth, wetted permeter, hydraul radus, and hydraul depth. A = BY +ZY = 0.0*.0+5.0*.0*.0=60.0 ft T= B+ZY=0 +.0*5.0*.0 = 40.0 ft P = B + Y 1+ Z = 0 + *.0 * = ft A 60.0 R = = = 1.49 ft P A 60.0 D = = = 1.5 ft T 40.0 Defnton of Slope 1. Channel Bottom Slope So. Water Surfae Slope Sw 3. Energy Slope Se 4. Frton Slope S f 14

15 Empral Equatons Mannng s Eq s dmensonally nonsstent, but most wdely aepted and used for hannel desgn. K= for feet-se or K=1 for meter-se. K U = n R 3 S K A K Q = UA = S A = A P 3 n P n S Use the bottom slope to produe the normal depth (unform flow) Use the energy slope to predt the flow depth (non-unform flow) Man-made Channels Cross Waves Unform Flow Super Elevaton on Outer Bank 15

16 Prsmat Channel Unformty n Algnment Straght Constant Cross Seton Constant Channel Slope Constant Channel Roughness It takes a long dstane to develop unform flow Normal Flow 1. Let S e =S o to fnd Y=Y n. Froude Number A trapezodal hannel arres a dsharge of 300 fs. The hannel has a slope of 0.005, roughness of 0.03, bottom wdth of 5 ft, and sde slope of 1V:ZH, Z=.0. Determne the normal depth. A n = Yn( 5 + Yn ) P = 5 + Y 1+ = Y n n n / 3 / 3 = [ Y n(5 + Y n )] ( Y n ) Q So we have Y 391ft 08 n = 3.91 ft, A n =50.08 ft, T n =0.63 ft, and U n = fps. A D = = =.43 feet T F r = = 0.68 < 1.0. Subrtal flow!

17 Example of Wer and Channel Flow Determne the flow from the wer measurement Calulate the normal flow ondton downstream Spef Energy=Y+U /g 1. Illustraton-- Slue gate (ΔE=0). For a gven Q, the urve for Y vs Es 3. Flow regmes 4. Ct Crtal lflow 5. Inrease or derease of Q 17

18 Example for Spef Energy Curve SPECIFIC ENERGY CURVE FOR TRAPEZOIDAL CHANNEL Bottom Wdth B= feet Left Sde Slope Z1= 3.00 ft/ft Rght Sde Slope Z= 3.00 ft/ft Desgn Flow Q= 100 fs Begnnng Flow Depth Y= 0.50 ft Inremental Depth Dy= 0.5 ft Flow Flow Top Flow Knet Sp. Froude Depth Area Wdth Veloty Energy Energy Numer Y A T u u^/g Es Fr ft sq ft ft fps ft ft Flow Depth n ft Spef Energy Es n feet Applaton of Energy Eq---Slue Gate Flow Flow Wetted Hy- Flow Flow Froude Sp Depth to Sp Depth Area P-meter Radus Veloty rate Numer Energy Centrod Fore Y A P R U Q Fr Es Yh Fs ft sq ft ft ft fps fs ft ft klb Flow Flow Top Flow Knet Sp. Froude Depth Area Wdth Veloty Energy Energy Numer Y A T u u^/g Es Fr ft sq ft ft fps ft ft

19 Crtal Flow Fr= Froude number = 1. Crtal flow depth 3. Crtal Slope s solved by Mannng s eq wth Yn=Y 4. Mld Slope and Steep Slope 1. Bottom Wdth B. Sde Slope Z 3. Top Wdth T = B + Z Y 4. Area A = 0.5 (T +B)Y 5. Hydraul Depth D = A /T 6. Froude Number Fr = U /(gd ) 0.5 =1.0 Q T F = = 1.0 r ga3 K A 3 K 5 Q = UA = S A = A 3 P 3 n P n S Example for Crtal Flow Gven Desgn Informaton: Fnd Crtal Slope Bottom Wdth B= 5.00 feet Bottom Wdth B= 5.00 feet Left Sde Slope Z1= 3.00 ft/ft Left Sde Slope Z1= 3.00 ft/ft Rght Sde Slope Z= 3.00 ft/ft Rght Sde Slope Z= 3.00 ft/ft Mannng's n N= Mannng's n N= Longtudnal Slope S= ft/ft Longtudnal Slope S= ft/ft Desgn Flow Q= fs Desgn Flow Q= fs Normal Flow Condton Normal Flow Depth Yn= 4.7 feet Normal Flow Depth Yn= 3.68 feet Wetted Peremeter P= 3.0 ft/ft Wetted Peremeter P= 8.7 ft/ft Normal Flow Area An= 76.1 sq ft Normal Flow Area An= sq ft Hydraul Radus R=.38 feet Hydraul Radus R=.09 feet Froude Number Fr= 0.73 Froude Number Fr= 1.01 Dfferene In Q dq= 0.00 ft/ft Dfferene In Q dq= 0.00 ft/ft Crtal Flow Condton: Crtal Depth Y= 3.68 feet Crtal Top Wdth T= 7.06 feet Crtal Flow Area A= sq ft Froude Number Fr= 1.01 F = r Q T ga 3 = 1.0 K A 3 K 5 Q = UA = S A = A 3 P 3 n P n S 19

20 Spef Fore 1. Illustraton -- Jump (ΔF=0). For a gven Q, the urve for Y vs Fs 3. Flow regmes 4. Crtal Flow 5. Inrease or derease of Q Y o Example for Spef Fore Curve SPECIFIC FORCE CURVE FOR TRAPEZOIDAL CHANNEL Bottom Wdth B= feet Left Sde Slope Z1= 3.00 ft/ft Rght Sde Slope Z= 3.00 ft/ft Y o Desgn Flow Q= 100 fs Begnnng Flow Depth Y 0.5 ft Inremental Depth Dy= 0.5 ft Flow Flow Top Central Flow Sp. Froude SP Depth Area Wdth Depth Veloty Fore Numer Energy Y A T Yo u Fs Fr Es ft sq ft ft ft fps Klbs ft Flow Depth n ft Spef Fore Fs n Klb 0

21 Applaton of Fore Eq---Jump Flow Flow Wetted Hy- Flow Flow Froude Sp Depth to Sp Depth Area P-meter Radus Veloty rate Numer Energy Centrod Fore Y A P R U Q Fr Es Yh Fs ft sq ft ft ft fps fs ft ft klb Flow Flow Top Central Flow Sp. Froude SP Depth Area Wdth Depth Veloty Fore Numer Energy Y A T Yo u Fs Fr Es ft sq ft ft ft fps Klbs ft Hydraul Jump: from superrtal to subrtal flow 1

22 PUMP DESIGN Pump Pump = mehan energy onverted to flud energy Output energy = effeny x Input energy Pump Desgn by Dr. James Guo, UC-Denver

23 Pump Head and Unts H hp = H H f A pump s dentfed by ts rotatng speed, power, and effeny. γqh p Horse Power Hp = for ft-seond unts where Hp n horse power = 550 lb-ft, 550η γqh p Klowatts Kw = for meter-seond unts. One Horse Power = Kw 1000η Pump Net Postve Suton Head Fnd Suton Head. H + SutonHea d = H + Losses H n pump + pump = P vapor γ Patm H n = + Z γ + Z n pump pump V + g to Pump 3

24 Pump Net Requred Dsharge Head Fnd Dsharge Head. H pump + Dsh arg ehead = Hout + Losses From Pump H pump P = γ vapor Patm H Out = + Z γ + Z Out pump pump V + g Desgn Pump Head and Horsepower Fnd Pump Head H n + h p = H out + InflowLoss + OutflowLos s Fnd the pump head wth Q= fs Is the pump head equal to suton head + dsharge head? Why do we have to alulate suton and dsharge heads? 4

25 Affnty Law Pump Model and Prototype 1. Bas Data Model Pump Dameter D feet Pump Rotatonal Speed n rpm Proto-type Pump Dameter D.00 feet Pump Rotatonal t Speed n rpm. Pump Affnty and Smlarty Laws: Proto-type to Model Ratos Rotatonal speed rato n*=n/n Dameter rato D*=D/D1.00 Head rato h*=h/h Flow rato Q*=Q/Q Power rato P*=P/P Performane Curve (Model Pump) Flow rate n fs 3. Pump Performane Curve Enter model pump urve: Flowrate fs Pumphead feet Calulate Proto-type pump urve Flowrate fs Pumphead feet Pump head n feet Pump Desgn by Dr. James Guo, UC-Denver 5

26 Pump n seres or n parallel Calulate Proto-type pump urve Flowrate fs Pumphead feet Pump Performane Curve for multple pumps Flowrate Number of Pump n Seres Pumphead Number of Pump n Parallel Q Hp fs Pump head n feet, Hp feet Flow rate n fs, Q A and Q 6